On comass and stable systolic inequalities

TL;DR

This paper investigates the maximum ratio of Euclidean to comass norms for p-covectors and establishes improved bounds, also proving stable systolic inequalities for manifolds with cohomology classes as cup products.

Contribution

It provides new upper bounds for the ratio of Euclidean to comass norms and extends stable systolic inequalities to specific cohomology classes.

Findings

Improved upper bounds for the Euclidean/comass ratio of p-covectors.

Established stable systolic inequalities for manifolds with cup product cohomology classes.

Enhanced understanding of geometric inequalities in Euclidean spaces.

Abstract

We study the maximum ratio of the Euclidean norm to the comass norm of p-covectors in Euclidean n-space and improve the known upper bound found in the standard references by Whitney and Federer. We go on to prove stable systolic inequalities when the fundamental cohomology class of the manifold is a cup product of forms of lower degree.